Gear measurement center motion control method and control system

Abstract

The invention discloses a gear measurement center motion control method and system, and relates to the technical field of gear measurement center motion control, and the method comprises the steps: building a kinematic model of a gear measurement center, and carrying out the coordinate transformation between a machine tool coordinate system and a workpiece coordinate system; establishing an electromechanical coupling control model; constructing a contour error calculation model, and decoupling a contour error and a trajectory tracking error; designing a single-axis position loop P control and speed feedforward combined composite controller; and designing a cross-coupling coordination controller based on the contour error model, generating real-time compensation amounts for the X axis and the theta axis by using the contour error and the trajectory tracking error through PID control, and feeding back the real-time compensation amounts to a single-axis controller to realize closed-loop compensation of multi-axis coordination motion. The system comprises a motion control unit, a coordination control unit, an error calculation unit and a servo driving unit. According to the method, the problem of contour errors caused by multi-axis dynamic response differences and nonlinear coupling is effectively solved, and the contour tracking precision is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of gear measuring center motion control, in particular to a gear measuring center motion control method and a control system. BACKGROUND

[0002] The gear measuring center is an important equipment for gear detection, and its measurement performance directly determines the control ability of gear manufacturing quality. Due to the complex and diversified trend of the profile of the measured workpiece, the measurement capability of the traditional gear measuring center has been unable to meet the demand; in the measurement scene of complex surfaces such as involute tooth profile, the measurement task of complex profile needs to rely on four-axis cooperative motion. At present, gear measurement has shifted from scanning measurement of simple feature points to high-precision scanning measurement of the entire tooth surface, and the demand for the integrity of tooth surface data and measurement efficiency is increasing. However, the existing measurement technology still has limitations in processing complex trajectories, such as low efficiency of contact measurement, difficulty in covering the root of the tooth and other special positions, and easy to exceed the tracking error limit in high-speed measurement.

[0003] Motion control technology is the main factor determining the accuracy of the gear measuring center. In the early stage, the single-axis servo position control was the basis of the motion control system of the gear measuring center; in order to optimize the steady-state performance and improve the dynamic response speed and positioning accuracy of the motion system, the motion control system of the gear measuring center is no longer limited to single-axis position control, but gradually shifts to dual-axis motion control. Subsequently, dual-axis tracking control focuses on optimizing the steady-state performance, and strives to improve the dynamic response speed and positioning accuracy; further, in order to make up for the shortcomings of single-axis control strategy in high-precision gear measurement, and the defects that dual-axis motion control is difficult to realize complex trajectory tracking, the motion control strategy of gear measuring instruments gradually develops towards multi-axis coordinated control. In this process, cross-coupling control as a new type of multi-axis cooperative control method can effectively improve the synchronization and tracking accuracy of the system, and is an important means to break through the difficulties of multi-axis cooperative control.

[0004] When the gear measuring center actually measures, it is often linked with rotary shafts and linear motion shafts, so the coupling error modeling focuses on the cross-axis influence in multi-axis cooperative motion, which mainly quantifies the error interference of the motion of a certain axis on other axes, provides real-time error feedback basis for the coordinated control algorithm, and thus directly affects the multi-axis synchronization accuracy.

[0005] With the improvement of gear manufacturing and detection requirements, the motion control performance improvement technology of gear measuring instruments has attracted much attention in recent years. At the same time, in order to reduce the profile error and improve the measurement capability of the instrument for complex tooth profile, multi-axis coordinated control technology has gradually become a research hotspot. SUMMARY

[0006] To address the aforementioned technical problems, this invention provides a motion control method and control system for a gear measurement center. By combining single-axis feedforward control with multi-axis cross-coupling coordinated control, the contour error during multi-axis linkage is reduced, thereby improving the accuracy of gear measurement.

[0007] To solve the above-mentioned technical problems, the technical solution proposed by this invention is as follows:

[0008] A motion control method for a gear measuring center, wherein the gear measuring center has three linear motion axes (X, Y, and Z) and a rotational axis (θ) about the Z-axis, the control method comprising:

[0009] Step S1: Establish the kinematic model of the gear measurement center. The kinematic model describes the coordinate transformation relationship between the probe in the machine tool coordinate system and the workpiece coordinate system based on the homogeneous coordinate transformation matrix.

[0010] Step S2: Design a single-axis motion control scheme, adopting a three-loop control structure of position loop, velocity loop and current loop, and introduce velocity feedforward compensation in the position loop;

[0011] Step S3: Design a multi-axis coordinated motion control scheme, construct a contour error calculation model, and input the calculated contour error and trajectory tracking error into the cross-coupled coordinated controller. This controller is used to calculate the contour error and trajectory tracking error under the linkage motion based on the single-axis tracking error, generate the error compensation amount for each motion axis, and feed it back to the single-axis control input.

[0012] A further improvement to the above technical solution is as follows:

[0013] Preferably, in step S1, the position transformations in the X, Y, and Z directions are performed using translation transformation matrices. , and The position on the θ-axis can be represented by a rotation transformation matrix. The homogeneous coordinate transformation matrix of the gear measurement center is:

[0014]

[0015]

[0016] in, This represents the coordinate transformation matrix that transforms the probe coordinates from the machine tool coordinate system to the workpiece coordinate system.

[0017] Preferably, in step S2, the position loop employs a P controller and velocity feedforward compensation; the position controller uses P control, and the velocity loop is equivalent to a first-order inertial element.

[0018]

[0019] Among them, K sp For the open-loop gain of the velocity loop, T sp Let be the velocity loop time constant, and the transfer function of the position loop tracking error be:

[0020]

[0021] Where L is the lead of the lead screw. This indicates the gain of the position loop proportional controller. Represents the complex frequency variable in the Laplace transform;

[0022] The transfer function for speed feedforward control is:

[0023] .

[0024] Preferably, in step S3, the coupling coordination controller first inputs the single-axis tracking error into the coupling controller to calculate the contour error and trajectory tracking error respectively; then, the PID controller performs closed-loop control on both with zero error as the target to obtain the error compensation amount of the linear axis and the rotary axis.

[0025] Preferably, the trajectory tracking error is obtained in step S3 as follows:

[0026] The trajectory equation of the theoretical involute tooth profile is as follows:

[0027]

[0028] The constant R is the base circle radius of the gear being measured. and These are the trajectory parameters linked to the X-axis and θ-axis;

[0029] The formula for calculating the contour error of the involute measurement trajectory is:

[0030]

[0031] The formula for calculating the trajectory tracking error of an involute measurement trajectory is:

[0032]

[0033] in, and This represents the location of the actual trajectory point.

[0034] Preferably, the single-axis tracking error is obtained as follows: Let the target trajectory point of the linkage axis be (X... d θ d When ), the actual feedback obtained is the trajectory point (X). a θ aThen, the two-axis tracking error is defined as:

[0035]

[0036] in, The tracking error is the θ-axis. This represents the tracking error along the X-axis.

[0037] The present invention also provides a control system for the motion of a gear measuring center, for the execution of the above control method, the control system comprising a coordination control unit, a motion control unit, an error calculation unit and a servo drive unit;

[0038] The coordination and control unit is responsible for executing the multi-axis cooperative strategy. It receives the actual and commanded positions of each axis from the motion control unit, calculates the tracking error, solves the contour error and trajectory tracking error, runs the cross-coupling control algorithm, and generates coordination compensation commands for each motion axis.

[0039] The motion control unit is the execution layer that directly controls the movement of each motor. It receives instructions from the coordination control unit and achieves high-precision single-axis control.

[0040] The motion control unit is implemented by a control module within a multi-axis motion control card or a distributed servo driver;

[0041] The error calculation unit provides algorithmic support for other units;

[0042] The servo drive unit converts the weak electrical control signals from the motion control unit into strong electrical power signals that can drive the motor.

[0043] Preferably, the motion control unit includes:

[0044] Feedforward compensation module: performs differential calculations on the input position command to generate a velocity feedforward signal;

[0045] Single-axis position controller: Receives position commands, compares them with feedback positions, and generates speed commands;

[0046] Single-axis speed controller: Receives speed commands, compares them with feedback speeds, and generates current commands;

[0047] Single-axis current controller: Receives current commands and generates a voltage signal to drive the motor through PWM modulation;

[0048] Feedback interface circuit: Connects to and processes signals from the encoder and grating ruler.

[0049] The gear measurement center motion control method and control system provided by this invention have the following advantages compared with the prior art:

[0050] (1) The gear measurement center motion control method and control system of the present invention adopts a composite control strategy of "single-axis feedforward to improve tracking accuracy + multi-axis cross-coupling to suppress contour error". The speed feedforward effectively reduces the dynamic lag of the single axis, providing a good foundation for collaborative control; the cross-coupling control directly compensates for the essential error (contour error) of multi-axis linkage in a closed loop, optimizing the synchronization performance at the system level.

[0051] (2) The gear measurement center motion control method and control system of the present invention combine single-axis feedforward control with multi-axis coordinated control based on cross-coupling. The single-axis feedforward control effectively improves the dynamic tracking accuracy of each axis and reduces tracking error from the source. The cross-coupling coordinated controller, on the other hand, performs dynamic compensation based on the contour error calculated in real time at the system level, effectively suppressing the contour error caused by the asynchrony between axes.

[0052] (3) The gear measurement center motion control method and control system of the present invention can accurately decouple and quantify the contour error by establishing an accurate XY-Zθ four-axis kinematic model and contour error calculation model (especially for the polar coordinate model of linear-rotation axis linkage), providing an accurate compensation basis for the coordination controller. Attached Figure Description

[0053] Figure 1 This is a diagram of the three-level closed-loop control architecture of the present invention.

[0054] Figure 2 The simplified transfer function block diagram for the position loop of this invention is shown below.

[0055] Figure 3 (a) is a comparison curve of trajectory tracking between open-loop and closed-loop control of the X-axis in the experimental verification of this invention.

[0056] Figure 3 (b) is a comparison curve of the tracking error between open-loop and closed-loop control of the X-axis in the experimental verification of this invention.

[0057] Figure 4 (a) is the involute trajectory tracking curve at a rotational speed of 0.6 r / min in the experimental verification of this invention.

[0058] Figure 4 (b) is the open-loop tracking error of the involute trajectory at a rotational speed of 0.6 r / min in the experimental verification of this invention.

[0059] Figure 5 (a) is the involute trajectory tracking curve at a rotational speed of 0.75 r / min in the experimental verification of this invention.

[0060] Figure 5 (b) is the open-loop tracking error of the involute trajectory at a rotational speed of 0.75 r / min in the experimental verification of this invention.

[0061] Figure 6 (a) is the involute trajectory tracking curve at a rotational speed of 1.5 r / min in the experimental verification of this invention.

[0062] Figure 6 (b) is the open-loop tracking error of the involute trajectory at a rotational speed of 1.5 r / min in the experimental verification of this invention.

[0063] Figure 7 (a) is a comparison curve of involute trajectory tracking between open-loop and coordinated control in the experimental verification of this invention.

[0064] Figure 7 (b) Comparison of involute trajectory tracking errors between open-loop and coordinated control in the experimental verification of this invention. Detailed Implementation

[0065] The following provides a detailed description of specific embodiments of the present invention. It should be understood that the specific embodiments described herein are for illustrative and explanatory purposes only and are not intended to limit the scope of the invention.

[0066] like Figure 1 As shown, the motion control method for gear measurement centers of the present invention is applicable to gear measurement centers with four-axis linkage (XY-Zθ). For single-axis motion control, this method introduces a speed feedforward compensation mechanism based on the traditional three-loop control architecture of current loop-velocity loop-position loop. Feedforward compensation predicts the motion trend to suppress single-axis following error, laying the foundation for high-precision single-axis control for multi-axis coordinated control. For multi-axis coordinated control, a cross-coupled coordinated controller is designed based on the error model of the involute measurement trajectory. This controller first decouples the contour error and trajectory tracking error from the single-axis tracking error, then generates real-time compensation quantities for the X and θ axes through a PID controller, and feeds the compensation quantities back to the input of the single-axis controller, achieving closed-loop optimization of multi-axis coordinated control.

[0067] The motion control method for the gear measurement center of the present invention comprises the following specific steps:

[0068] Step S1: Construct a kinematic model.

[0069] Establish the coordinate transformation relationship from the machine tool coordinate system (MCS) to the workpiece coordinate system (WCS), and use the coordinate method to establish the kinematic model of the gear measurement center. The independent motion of the probe and the workpiece in the machine tool coordinate system will be converted into the composite motion trajectory of the probe in the workpiece coordinate system.

[0070] S1-1, The kinematic model of the gear measurement center is established using the coordinate method:

[0071] The gear measurement center needs to coordinate the linear motion of the X, Y, and Z axes with the rotational motion of the θ axis to achieve accurate tracking of the measurement trajectory by the measuring probe. X is the tangential motion of the gear circumference, Y is the radial motion of the gear, Z is the axial motion of the gear, and θ is the rotational motion of the gear. The kinematic model can be characterized as a composite coordinate system composed of the three orthogonal linear motion axes X, Y, and Z and the rotation axis θ.

[0072] Calculate the coordinate transformation matrix for transforming the probe coordinates from the machine tool coordinate system to the workpiece coordinate system. Then, using forward kinematics, the final coordinates of the probe in the workpiece coordinate system under different working conditions are calculated; subsequently, using matrix... Derive the inverse transformation matrix The inverse kinematics solution is then performed, and the correctness of the kinematic model is verified by the results of the forward and inverse kinematics solutions.

[0073] The XY-Zθ configuration gear measuring center has four degrees of freedom: X, Y, and Z are translational degrees of freedom, and θ is the rotational degree of freedom along the Z-axis. The probe has X and Y degrees of freedom in the instrument coordinate system, while the workpiece coordinate system has Z and θ degrees of freedom relative to the instrument coordinate system. Therefore, the probe has four degrees of freedom relative to the workpiece coordinate system: X, Y, Z, and θ. That is, the probe can move along these four directions in the workpiece coordinate system. According to the theory of homogeneous coordinate transformation, the position transformations in the X, Y, and Z directions are represented by translation transformation matrices. , and The position on the θ-axis can be represented by a rotation transformation matrix. The homogeneous coordinate transformation matrix of the gear measurement center is:

[0074]

[0075]

[0076] S1-2, Establish the control model for the gear measurement center:

[0077] The linear motion axis of the gear measuring center converts the rotational motion of the motor into the linear motion of the worktable via a ball screw. The conversion relationship is as follows:

[0078]

[0079] Where, q i P is the linear displacement of the worktable. i Let θ be the lead screw pitch. mi For the motor rotation angle, is the conversion factor, representing the linear displacement of the worktable corresponding to each radian of motor rotation.

[0080] The system state variables are and The state equation of the linear motion system is:

[0081]

[0082] in, This refers to the motor speed. This is the position output of the linear motion system. The transfer function of the controlled object's model is:

[0083]

[0084] in, This is the representation of the torque current command sent by the control system to the current loop in the complex frequency domain. The total moment of inertia (including motor inertia, lead screw inertia, and the equivalent moment of inertia of the load mass converted to the motor shaft). It is the total coefficient (including rotational damping and the equivalent damping of linear friction converted to the rotating axis). Let be the torque constant of the motor. is the complex frequency variable in the Laplace transform.

[0085] Step S2: Single-axis motion control of the gear measuring center.

[0086] A three-level closed-loop control architecture (such as current loop-speed loop-position loop) is adopted. Figure 1 As shown in the figure, the position control stage integrates a feedforward compensation algorithm, which effectively suppresses the following error through predictive control, thereby achieving micron-level motion tracking accuracy.

[0087] The functions and control methods of each loop in the three-loop architecture (current loop-velocity loop-position loop) include the following:

[0088] S2-1, Current Loop: Suppresses current ripple and grid disturbances, employs a PI controller, and its bandwidth is designed to be the motor's electrical time constant. Eight times (1kHz) to ensure fast current tracking of commands, the sampling frequency is set to 10kHz, and sampling noise is eliminated by first-order RC filtering (cutoff frequency 2kHz).

[0089] S2-2, Speed ​​Loop: Connects the current loop and the position loop, suppresses load disturbances (such as measuring torque changes), and uses a PI controller to determine parameters through empirical tuning.

[0090] First adjust the proportional coefficient Once the critical oscillation (overshoot 5%) is reached, the integral coefficient K is adjusted again. vi After eliminating steady-state error, the final parameter is K. vp = 0.5, K vi= 10, bandwidth is set to 200Hz (far lower than the current loop to avoid inter-loop coupling).

[0091] S2-3, Position Loop: Achieves precise positioning and trajectory tracking by using a P controller and velocity feedforward compensation. The P controller ensures steady-state accuracy, while the velocity feedforward compensation suppresses dynamic following errors.

[0092] To facilitate the analysis of single-axis tracking error, Figure 1 Simplified to Figure 2 The position controller uses P control, and the velocity loop is equivalent to a first-order inertial element.

[0093]

[0094] Among them, K sp The open-loop gain of the velocity loop (by K) vp Torque coefficient K T The derivation yields 110), T sp Given the speed loop time constant (0.8 ms calculated from the bandwidth), the transfer function of the permanent magnet synchronous motor is: Therefore, the transfer function of the position loop tracking error can be obtained as follows:

[0095]

[0096] Where L is the lead of the lead screw. This indicates the gain of the position loop proportional controller. This represents the complex frequency variable in the Laplace transform.

[0097] The transfer function for speed feedforward control is:

[0098] .

[0099] Step S3: Coordinate motion control of the gear measuring center.

[0100] S3-1, Involute Measurement Trajectory Measurement Model: When the probe moves from the initial position to the instantaneous position, its linear displacement is... Let θ be the angle of rotation of the measured involute tooth profile about the rotation center O. The mathematical model for measuring the involute tooth profile using the XY-Zθ gear measuring center is as follows:

[0101]

[0102] in, Indicates the base circle radius of the gear. This indicates the involute development angle.

[0103] S3-2, Construction of the error model for involute tooth profile measurement trajectory:

[0104] The trajectory equation of the theoretical involute tooth profile is as follows:

[0105]

[0106] The constant R is the base circle radius of the gear being measured. and These are the trajectory parameters linked to the X-axis and θ-axis.

[0107] The formula for calculating the contour error of the involute measurement trajectory is:

[0108]

[0109] The formula for calculating the trajectory tracking error of an involute measurement trajectory is:

[0110]

[0111] in, and This represents the location of the actual trajectory point.

[0112] S3-3, X-θ coordinated control:

[0113] Based on single-axis motion control, a coupled control method is used for contour error compensation control to reduce contour error. The schematic diagram of the coupled controller involves first inputting the single-axis tracking error into the coupled controller, and then calculating the contour error E. e Tracking error E t Then, closed-loop control of both axes is performed in the PID controller with zero error as the target, and the error compensation amounts for the linear and rotary axes are obtained. and Then, these values ​​are compensated separately and fed into the input commands of the single-axis controller to generate additional compensation in real time.

[0114] S3-3-1, Error Acquisition: Let the target trajectory point of the linkage axis be (X... d θ d When ), the actual feedback obtained is the trajectory point (X). a θ a Then, the two-axis tracking error is defined as:

[0115]

[0116] S3-3-2, Error Decoupling: G x and G c Let be the coupling gains of the linear motion axis and the rotary axis coupling controller, respectively. Then:

[0117]

[0118] in, The tracking error is the θ-axis. This represents the tracking error along the X-axis.

[0119] S3-3-3, Compensation Quantity Generation: The gear measurement center adopts a single-axis feedforward-cross-coupling control scheme. In this scheme, each motion axis uses a position feedforward control method to improve the single-axis motion control accuracy and reduce the single-axis control error. At the same time, a cross-coupling coordinated motion control method is adopted. The compensation quantity of each motion axis during the synchronous motion of the two axes is decoupled through the contour error calculation model. Finally, the PID controller compensates each motion axis in the form of position compensation to reduce the relative error between axes and achieve the control effect of multi-axis synchronous motion.

[0120] S3-3-4, Compensation Injection: The motion of each axis of the gear measuring center is relatively independent. The X-axis and Y-axis linear motion guides together form the probe's horizontal motion platform, and the Z-axis and θ together form the workpiece motion platform. The motion between the two motion platforms is independent of each other. Each axis has its own servo control system, and the coordinated motion controller only acts on the axes that need to move simultaneously.

[0121] Taking involute trajectory tracking control as an example, the gear measurement center needs the X-axis and θ-axis to move together to measure the involute trajectory. At this time, the coordinated motion controller acts on the X-axis and θ-axis. The measurement system transmits the error signals of the X-axis and θ-axis to the coordinated motion controller. The coordinated motion controller then calculates the compensation amount of the X-axis and θ-axis through the single-axis error and transmits the compensation to the input signals of the X-axis and θ-axis in the form of position compensation.

[0122] The present invention also provides a control system for the above-described control method, which adopts a hierarchical and modular design, including: a coordination control unit, a motion control unit, an error calculation unit, and a servo drive unit.

[0123] In this embodiment, the coordination control unit is the core decision-making layer of the entire system, responsible for executing the multi-axis coordination strategy. It receives the actual and commanded positions of each axis from the motion control unit, calculates the tracking error, calls the model in the error calculation unit to solve the contour error and trajectory tracking error in real time, runs the cross-coupling control algorithm to generate coordination compensation commands for each motion axis, and manages complex measurement trajectory planning and multi-axis synchronization logic.

[0124] In this embodiment, the motion control unit is the execution layer that directly controls the movement of each motor. It receives instructions from the coordination control unit and achieves high-precision single-axis control. It receives the final position command from the coordination control unit, which has been superimposed with compensation; executes the single-axis position loop, speed loop, and current loop closed-loop control algorithm; sends specific control signals (such as PWM waves and analog voltage commands) to the servo drive unit; and collects position and speed information from feedback elements such as motor encoders and grating rulers.

[0125] The motion control unit is implemented by a control module within a multi-axis motion control card or a distributed servo drive. It includes:

[0126] Feedforward compensation module: performs differential calculations on the input position command to generate a velocity feedforward signal;

[0127] Single-axis position controller (P control): Receives position commands (including feedforward and coordinated compensation), compares them with the feedback position, and generates speed commands;

[0128] Single-axis speed controller (PI control): Receives speed command, compares it with feedback speed, and generates current (torque) command;

[0129] Single-axis current controller (PI control): Receives current commands and generates a voltage signal to drive the motor through PWM modulation;

[0130] Feedback interface circuit: Connects to and processes signals from the encoder and grating ruler.

[0131] In this embodiment, the error calculation unit is the system's "mathematical model library," providing algorithmic support for other units. It stores and executes forward and inverse kinematic transformation matrices; stores and executes contour error calculation models for straight and curved trajectories (especially involutes); and provides calculation functions for intermediate variables.

[0132] The error calculation unit is an independent software module (such as a dynamic link library) embedded in the software of the coordination control unit; it can also be the algorithm logic embedded in the motion control unit. It is tightly connected to the coordination control unit and the motion control unit through a data bus or function call interface, providing calculation services on demand.

[0133] In this embodiment, the servo drive unit is the power execution layer of the system. The servo drive unit converts the weak current control signals sent by the motion control unit into strong current power signals that can drive the motor to operate; it realizes closed-loop current control of the motor and protects circuit safety.

[0134] For the X, Y, and Z linear axes: a permanent magnet synchronous servo motor (PMSM) is used, which converts rotary motion into linear motion through a ball screw pair. The servo driver receives current / speed commands from the motion control unit and drives the PMSM.

[0135] For the θ-axis rotation: a direct-drive torque motor (DD Motor) is used. Its driver directly receives control commands from the motion control unit, driving the motor rotor to precisely rotate the workpiece platform, without any intermediate transmission links.

[0136] All servo drives are connected to the motion control unit via fieldbus (such as EtherCAT, PROFINET) or analog / pulse interface to receive commands and upload status.

[0137] The workflow of the control system of this invention is as follows: The coordination control unit generates ideal trajectory points in the W-system based on the measurement task (such as scanning an involute segment), and converts them into motion command sequences for each axis in the M-system through inverse kinematics. These commands are then sent to the motion control unit. While executing single-axis P+ feedforward control, the motion control unit uploads the tracking errors of each axis to the coordination control unit in real time. The coordination control unit calls the error calculation unit to calculate the contour error based on the current error and the trajectory model, and generates a compensation amount through the cross-coupling controller, which is then sent to the motion control unit in real time to correct the commands for each axis. Finally, the servo drive unit drives the motor to perform precise coordinated motion, enabling the probe to track the theoretical tooth profile with high precision.

[0138] Experimental verification

[0139] The experiment consists of two main parts:

[0140] (1) Open-loop trajectory tracking experiment

[0141] Trajectory tracking tests were conducted on involute trajectories without controlling the coordination between axes. Three different θ-axis tracking speeds (0.6 r / min, 0.75 r / min, and 1.5 r / min) were set up for the experiment, and multiple independent repeats were performed. Experimental data were collected at 10 ms intervals, including time, theoretical and measured coordinates of the X-axis and θ-axis. Analysis of the experiment showed that the system entered a steady-state motion when the rotation angle θ reached 1.5° or higher. Therefore, subsequent analysis only focused on data with θ in the range of 1.5° to 36°, including initial data removal, coordinate transformation calculation, calculation of contour error evaluation indicators, and plotting of contour error point-line graphs.

[0142] (2) Coordinated motion trajectory tracking and control experiment

[0143] Trajectory tracking tests were conducted using a cross-coupled coordinated controller. A constant velocity of 0.6 r / min, which performed well in the open-loop experiment, was selected, and data was collected at 10 ms intervals. The experimental results will be used to evaluate the effectiveness of the coordinated controller in improving contour error.

[0144] The results are analyzed as follows:

[0145] (1) Results of single-axis tracking experiment

[0146] Single-axis tracking experiments were conducted on the X-axis and θ-axis. The tracking effects of the two axes were similar, so the tracking effect of the X-axis was chosen to be shown for simplification.Figure 3 The figure illustrates the X-axis tracking error and its effect after implementing open-loop control and adding a coordinating controller. As can be seen from the figure, the tracking accuracy is improved by a factor of three due to the coordinating controller.

[0147] Table 1 summarizes the evaluation metrics for X-axis tracking error under different control methods. These metrics include the average tracking error of the X-axis (Etracking). Xm ), the root mean square error of the X-axis tracking error (E) Xv ), the standard deviation of the X-axis tracking error (E) Xs The minimum error of X-axis tracking error (E) X min ) and the maximum error of X-axis tracking error (E) X max By comparing the error indices of open-loop control and closed-loop control, the impact of the coordinated controller of this invention on improving tracking accuracy can be evaluated.

[0148] The results show that closed-loop control is more effective in reducing X-axis tracking error. Smaller standard deviations and root mean square errors indicate that closed-loop control not only reduces the average and maximum errors but also decreases the error fluctuation range. These findings confirm the effectiveness of the coordinated controller in improving system tracking accuracy.

[0149] Table 1. Evaluation Indicators for X-axis Tracking Error

[0150]

[0151] (2) Results of open-loop trajectory tracking experiment

[0152] Multi-axis control experiments were conducted to track involute tooth profile trajectories, helical trajectories, and elliptical trajectories. Experimental results show that the designed coordinated controller can significantly improve tracking accuracy under different trajectory types. In particular, the involute tooth profile trajectory, due to its complex geometric characteristics, places higher demands on the control system.

[0153] Given that the tracking performance of involute tooth profile trajectories is representative of the tracking performance of other trajectory types (helices and ellipses), and considering the similar trends in the tracking error changes of these trajectories, only the tracking performance of involute tooth profile trajectories is shown. This choice aims to avoid repetitive presentation of results and focus on discussing the scenarios most challenging to the control system performance. Trajectory tracking curves and tracking errors at different speeds are shown below. Figures 4 to 6 As shown, the trajectory tracking effect decreases with increasing measurement speed.

[0154] Table 2 Evaluation Indicators for Open-Loop Control Involute Profile Error

[0155]

[0156] Further analysis of the data in Table 2 reveals that when the rotational speed decreases from 1.5 r / min to 0.6 r / min, the average profile error decreases by approximately 50.04%, the maximum profile error by approximately 50.91%, the minimum profile error by approximately 49.70%, the profile error range by approximately 64.52%, the standard deviation by approximately 55.86%, and the root mean square error by approximately 48.84%. These experimental results demonstrate that tracking speed significantly affects the accuracy of the profile error. Higher tracking speeds significantly increase the tracking error of the trajectory. Therefore, 0.6 r / min, which performed best in the open-loop trajectory tracking experiment, was chosen as the tracking speed for the coordinated motion trajectory tracking control experiment.

[0157] (3) Results of the coordinated motion trajectory tracking control experiment

[0158] The coordinated motion controller designed in this method was used to conduct trajectory tracking experiments at a rotational speed of 0.6 r / min. The experimental results were then compared with those of open-loop trajectory tracking experiments at the same tracking speed of 0.6 r / min (e.g.,...). Figure 7 As shown in the figure, the results show that the contour error under the action of the coordinated controller is about 1 / 2 of the contour error under open-loop control. The coordinated controller proposed in this invention can effectively improve the trajectory tracking accuracy of multi-axis systems, especially when dealing with complex trajectories.

[0159] Table 3 Comparison of involute trajectory tracking errors under open-loop control and coordinated control

[0160]

[0161] Further analysis of the data in Table 3 reveals that coordinated control significantly improves involute trajectory tracking error compared to open-loop control. The average profile error is reduced by approximately 45.34%, the root mean square error of the profile error is reduced by 98.77%, and the minimum and maximum profile errors are reduced by 57.42% and 32.70%, respectively. However, the standard deviation of the profile error increases slightly by approximately 22.19%, indicating that the error distribution under coordinated control is more dispersed, but the overall error level remains significantly lower than that under open-loop control. These results demonstrate that coordinated control has a clear advantage in improving involute trajectory tracking accuracy, particularly in reducing the root mean square error and the minimum error.

[0162] The single-axis feedforward + cross-coupling control method designed in this invention can significantly improve the contour tracking performance of the measurement system.

[0163] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A motion control method for a gear measuring center, characterized in that, The gear measuring center has three linear motion axes (X, Y, and Z) and one θ axis (rotating around the Z axis). The control method includes: Step S1: Establish the kinematic model of the gear measurement center. The kinematic model describes the coordinate transformation relationship between the probe in the machine tool coordinate system and the workpiece coordinate system based on the homogeneous coordinate transformation matrix. Step S2: Design a single-axis motion control scheme, adopting a three-loop control structure of position loop, velocity loop and current loop, and introduce velocity feedforward compensation in the position loop; Step S3: Design a multi-axis coordinated motion control scheme, construct a contour error calculation model, and input the calculated contour error and trajectory tracking error into the cross-coupled coordinated controller. This controller is used to calculate the contour error and trajectory tracking error under the linkage motion based on the single-axis tracking error, generate the error compensation amount for each motion axis, and feed it back to the single-axis control input.

2. The gear measurement center motion control method according to claim 1, characterized in that, In step S1, the position transformation in the X, Y, and Z directions is performed using translation transformation matrices. , and The position on the θ-axis can be represented by a rotation transformation matrix. The homogeneous coordinate transformation matrix of the gear measurement center is: ； ； in, This represents the coordinate transformation matrix that transforms the probe coordinates from the machine tool coordinate system to the workpiece coordinate system.

3. The gear measurement center motion control method according to claim 2, characterized in that, In step S2, the position loop uses a P controller and velocity feedforward compensation; the position controller uses P control, and the velocity loop is equivalent to a first-order inertial element. ； Among them, K sp For the open-loop gain of the velocity loop, T sp Let be the velocity loop time constant, and the transfer function of the position loop tracking error be: ； Where L is the lead of the lead screw. This indicates the gain of the position loop proportional controller. Represents the complex frequency variable in the Laplace transform; The transfer function for speed feedforward control is: 。 4. The gear measuring center motion control method according to claim 1, characterized in that, In step S3, the coupling coordination controller first inputs the single-axis tracking error into the coupling controller to calculate the contour error and trajectory tracking error respectively; then, the PID controller performs closed-loop control on both with zero error as the target, and obtains the error compensation amount of the linear axis and the rotary axis.

5. The gear measuring center motion control method according to claim 4, characterized in that, The method for obtaining the trajectory tracking error in step S3 is as follows: The trajectory equation of the theoretical involute tooth profile is as follows: ； The constant R is the base circle radius of the gear being measured. and These are the trajectory parameters linked to the X-axis and θ-axis; The formula for calculating the contour error of the involute measurement trajectory is: ； The formula for calculating the trajectory tracking error of an involute measurement trajectory is: ； in, and This represents the location of the actual trajectory point.

6. The gear measuring center motion control method according to claim 5, characterized in that, The single-axis tracking error acquisition method is as follows: Let the target trajectory point of the linkage axis be (X... d θ d When ), the actual feedback obtained is the trajectory point (X). a θ a Then, the two-axis tracking error is defined as: ； in, The tracking error is the θ-axis. The tracking error is on the X-axis. The performance data obtained from the simulation is used as the fitness value to guide the population to evolve toward the optimization goal. After multiple iterations and convergence, the optimal solution is obtained.

7. A control system for measuring the motion of a gear measuring center, characterized in that, For execution of the control method of any one of claims 1 to 6, the control system includes a coordination control unit, a motion control unit, an error calculation unit, and a servo drive unit; The coordination and control unit is responsible for executing the multi-axis cooperative strategy. It receives the actual and commanded positions of each axis from the motion control unit, calculates the tracking error, solves the contour error and trajectory tracking error, runs the cross-coupling control algorithm, and generates coordination compensation commands for each motion axis. The motion control unit is the execution layer that directly controls the movement of each motor. It receives instructions from the coordination control unit and achieves high-precision single-axis control. The motion control unit is implemented by a control module within a multi-axis motion control card or a distributed servo driver; The error calculation unit provides algorithmic support for other units; The servo drive unit converts the weak electrical control signals from the motion control unit into strong electrical power signals that can drive the motor.

8. The gear measurement center motion control method according to claim 7, characterized in that, The motion control unit includes: Feedforward compensation module: performs differential calculations on the input position command to generate a velocity feedforward signal; Single-axis position controller: Receives position commands, compares them with feedback positions, and generates speed commands; Single-axis speed controller: Receives speed commands, compares them with feedback speeds, and generates current commands; Single-axis current controller: Receives current commands and generates a voltage signal to drive the motor through PWM modulation; Feedback interface circuit: Connects to and processes signals from the encoder and grating ruler.

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